Question

The graph of a relation is given. Apply the vertical line test to determine if this relation is a function. (1 point) Responses The relation is a half-circle. The relation is a half-circle. No, the given relation is not a function. No, the given relation is not a function. Yes, the given relation is a function. Yes, the given relation is a function. There is not enough information to determine whether this relation is a function.

The line creates a half circle on the right of the axis. From the top Y point to middle far right then Stops at the bottom Y point

Answer 1

To use the vertical line test to determine if a relation is a function, you need to check if any vertical line intersects the graph at more than one point.

In the case of a half-circle:

- If the half-circle is oriented in such a way that it is open at the bottom (i.e., it curves up and to the right), a vertical line drawn at any point within the width of the half-circle will intersect the graph only once.
- Therefore, because no vertical line can intersect the half-circle at more than one point, the relation **passes the vertical line test**.

Based on your description, where the half-circle extends from the top Y point down to the bottom Y point without continuing further on the left side (cut off at the axis), we conclude that it does pass the vertical line test.

Thus, you can state that:

**Yes, the given relation is a function.**